This invention relates to a method and apparatus for measuring the time difference between two events, where each event is represented by an electrical pulse capable of triggering a digital circuit. In particular, this invention relates to time measurement systems accurate to within 10 picoseconds.
High resolution time measurement systems are required in a number of applications. For example, a time measurement system may be used to determine the bit error rate in an information transmission device. Because the phase of a digital signal can be determined by measuring the time difference between transitions (zero crossing points) of the digital signal, a statistical analysis can be performed upon the measured times between transitions of the digital signal to determine the quality of the information transmission. In information transmission devices which operate at very high frequencies, the time differences between transitions of the digital signal is sometimes on the order of 50 picoseconds. Thus, it is important to employ a time measurement system with a very high resolution.
A further example of an application for a high resolution time measurement device is in the field of pulse transmission and reflection. To determine the location of a breach in a fiber optic line, for example, a light pulse is propagated down the length of the optical fiber. The light pulse is then reflected at the point where the breach is located, and is detected at the light source location a finite time later. In order to determine the location of the breach in the fiber optic line, a very precise measurement must be taken of the time between the transmission of the light, and the detection of the reflected light. Therefore it is advantageous to employ a high resolution time measurement device in such applications.
Present high resolution time measurement systems generally employ linear ramp waveforms as a reference signal from which to measure the time difference between two electrical events. An example of such a linear ramp waveform 100 is illustrated in FIG. 1. The linear ramp waveform 100 has an amplitude function y(t) which varies over time as shown. It should be noted, however, that the conventional method for determining the time difference between two electrical events using a linear ramp waveform is subject to inherent limitations. Namely, the accuracy of the measurements to determine the time difference between two electrical events is dependent upon the linearity of the function y(t).
The frequency spectrum of the function y(t) is given by its Fourier transform Y(.omega.), where EQU Y(.omega.)=.omega..sub.1 +(.omega..sub.2 /3.sup.2)+(.omega..sub.3 /5.sup.2)+. . .+.omega..sub.n /(2n-1).sup.2 ( 1)
where .omega..sub.i is the i-th harmonic of .omega.. The frequency spectrum of y(t) is an infinite series, so that a perfectly linear waveform is obtained as n approaches infinity. Thus, in order for y(t) to be perfectly linear, the function y(t) must contain an infinite number of sine wave harmonic components. Each harmonic is an integer multiple of the frequency of the fundamental, so that the range of frequencies (or bandwidth) required to implement a perfectly linear signal y(t) is infinite. Since this is not practically possible, the actual implementation of the function y(t) will have some degree of distortion.
Note that the distortion introduced when using a linear ramp waveform as a reference signal is a limitation inherent to the method used in determining the time difference between events. Even if the components used within the time measurement system were ideal, it would be impossible to generate an infinite number of sine wave harmonics needed to produce a perfectly linear waveform. This inherent limitation is significant because, as technological advancements are made in component design, the distortion introduced within time measurement systems which use linear ramp waveforms will include an additional factor due to the infinite bandwidth requirement. Therefore, with advancements in component design, the distortion introduced within a time measurement system which employs a linear ramp waveform as a reference signal will not decrease as quickly as the distortion introduced within time measurement systems which employ reference waveforms that require a finite number of harmonics.
To reduce the distortion inherent within y(t) (to make y(t) more linear), additional harmonics must be added. Therefore, to obtain a high degree of accuracy in a method using a linear ramp as a reference waveform, it is necessary to use a high signal bandwidth. However, in systems which use a high bandwidth signal as a reference waveform, actual distortions in the reference signal are difficult to predict and verify.
A need then exists for a high resolution time measurement device which can operate at a relatively low frequency, and which has a low bandwidth. A further need exists for an apparatus and method for measuring time between events to a very high accuracy, which incorporates a reference signal that has properties which are easily predicted and verified.